probability that a lamp in a classroom will burnt out will be 0.3. six lamps are fitted in the classroom. If it is known that the classroom is unusable if the number of lamps burning in it is less than four, find the probability that classroom can not used at random occasion
Answers
Given : probability that a lamp in a classroom will burnt out will be 0.3. six lamps are fitted in the classroom. If it is known that the classroom is unusable if the number of lamps burning in it is less than four,
To find : probability that classroom can not used at random occasion
Solution:
Probability of lamp burning p = 0.3
Probability of lamp not burning q = 1-0.3 = 0.7
Number of Lamps n = 6
P(x) = ⁿCₓpˣqⁿ⁻ˣ
classroom can not used if lamp burning are less than 4
Lamp burning are 0 , 1 , 2 & 3
= P (0) + P(1) + P(2) + P(3)
= ⁶C₀(0.3)⁰(0.7)⁶ + ⁶C₁(0.3)¹(0.7)⁵ + ⁶C₂(0.3)²(0.7)⁴ + ⁶C₃(0.3)³(0.7)³
= 0.117649 + 0.302526 + 0.324135 + 0.18522
= 0.762832
0.762832 is the probability that classroom can not used at random occasion
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